Bundles with fiberwise negatively curved metrics

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• Mauricio Bustamante, Augsburg
• Wednesday 21 February 2018, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

A smooth M-bundle is said to be negatively curved if its fibers are equipped with Riemannian metrics of negative sectional curvature, varying continuously from fiber to fiber. The difference between negatively curved M-bundles and smooth M-bundles is measured by the space of all negatively curved metrics on M. In this talk I will show that the latter space has non-trivial rational homotopy groups, provided certain dimension constraints are satisfied. Hence the two bundle theories generally differ. The results extend to other spaces of metrics, e.g. spaces of Riemannian metrics with geodesic flow of Anosov type. This is joint work with F.T. Farrell and Y. Jiang.

This talk is part of the Differential Geometry and Topology Seminar series.

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